# [Haskell-beginners] suggestions for optimizing sudoku solver

Peter Hall peter.hall at memorphic.com
Thu Jan 5 03:37:58 CET 2012

```Thanks, I have that book coming any day now :)

In the meantime, I started again and tried to avoid accessing the full
List-of-Lists inside the algorithm and to make it more linear. So now,
I'm starting with a list of hints (ie solved cells) and a list of
unsolved cells, each with an index for row, column and block. Each
recursion attempts to move a cell from the unresolved list to the
hints list.

https://github.com/peterjoel/sudoku/blob/master/src/Sudoku/Solver2.hs

The result is actually really simple, and far faster than I had
before. There are some other functions wrapping it, but this is the
meat of it:

solveNext :: [((Int,Int,Int),Int)] -> [(Int,Int,Int)] -> Maybe
[((Int,Int,Int),Int)]
solveNext hints [] = Just hints
solveNext hints (r@(x,y,b):rem) = case catMaybes \$ map try remaining of
[] -> Nothing
p:_ -> Just p
where try v = solveNext ((r,v):hints) rem
remaining = [1..9] \\ (map snd .
filter isNeighbour) hints
isNeighbour ((x',y',b'),_) = x==x' ||
y==y' || b==b'

For the two "hardest" grids (hard4.txt and hard5.txt) that were taking
my first solution 17-18 seconds to solve, it's now doing it in around
0.004 seconds, which is about 4000x faster! Strangely, some of the
easier ones are now taking slightly longer. For example this one:
https://github.com/peterjoel/sudoku/blob/master/data/hard2.txt , took
0.18s with Solver1, but 0.65s with Solver2. Still within reason
though.

Peter

On Wed, Jan 4, 2012 at 3:01 AM, KC <kc1956 at gmail.com> wrote:
> Bird begins with the specification (without regard to efficiency):
>
> solve = filter valid . expand . choices
>
> And ends up with this third version of solve
>
> solve = search . choices
>
> search m
>  | not (safe m) = []
>  | complete m' = [map (map head) m']
>  | otherwise = concat (map search (expand1 m'))
>  | where m' = prune m
>
> Note: some functions are missing
>
> The interesting idea is how he uses equational reasoning to reach this solve.
>
>
>
>
> On Sun, Jan 1, 2012 at 7:27 PM, Peter Hall <peter.hall at memorphic.com> wrote:
>> I set myself a learning task of writing a sudoku solver.
>> (https://github.com/peterjoel/sudoku/blob/master/src/Sudoku.hs)
>> It works pretty well, but struggles with some of the harder grids.
>> e.g. data/hard4.txt and data/hard5.txt take around 18 seconds to
>> solve. Obviously there's a limit, but I feel like I should be able to
>> make this faster.
>>
>> I think the main issue is reading/writing to the cells in the grid,
>> since (!!) is O(n). Even though it never has to go beyond index 8, it
>> will add up over the millions of times it has to do it. I imagine it
>> could be a lot faster if I use a static, non-list data structure, but
>> I was hoping to keep it a bit more flexible.
>>
>> Also, I'm struggling to get started with performance profiling. Can
>> someone point me to some good resources?
>>
>> Peter
>>
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